Halo teman! The simple difference here is that "gugup" is an adjective, so it cannot fit well with "bukan". Still, there would be some variations that can use "bukan". I think that replacing "gugup" with "orang yang gugup" (not necessarily doing the same with "tegang"), or with "penggugup" (noun, "a person who easily becomes nervous"), this sentence has a different construction, but a close meaning.

Saya bukan orang yang gugup, saya hanya tegang!

Saya bukan penggugup, saya hanya tenang!

I think these sentences translate as "I am not a nervous person, I am only tense!"

Wiktionary bahasa Indonesia

https://id.wiktionary.org/wiki/gugup

https://id.wiktionary.org/wiki/penggugup

I hope it helps.

Selamat belajar! :)